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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E20">Th20</font></span>: <a NAME="T20"><span class="comment"><font color="firebrick">:: SIMPLEX2:20</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">i</font>, <font color="Olive" title="b2">j</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <br/>  for <font color="Olive" title="b3">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Olive" title="b1">i</font></span>)</span>,<span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Olive" title="b2">j</font></span>)</span></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span>,<span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">i</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b2">j</font></span>)</span></span>)</span>  st (  for <font color="Olive" title="b4">fi</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Olive" title="b1">i</font></span>)</span><br/>  for <font color="Olive" title="b5">fj</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Olive" title="b2">j</font></span>)</span> holds  <font color="Olive" title="b3">f</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b4">fi</font>,<font color="Olive" title="b5">fj</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">fi</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b5">fj</font> ) holds <br/> for <font color="Olive" title="b4">r</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a><br/>  for <font color="Olive" title="b5">fi</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K14" title="EUCLID:func.14">Euclid</a> <font color="Olive" title="b1">i</font></span>)</span><br/>  for <font color="Olive" title="b6">fj</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K14" title="EUCLID:func.14">Euclid</a> <font color="Olive" title="b2">j</font></span>)</span><br/>  for <font color="Olive" title="b7">fij</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K14" title="EUCLID:func.14">Euclid</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">i</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b2">j</font></span>)</span></span>)</span>  st <font color="Olive" title="b7">fij</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">fi</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b6">fj</font> holds <br/><font color="Olive" title="b3">f</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1"><a href="borsuk_1.html#K3" title="BORSUK_1:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="euclid_9.html#K4" title="EUCLID_9:func.4">OpenHypercube</a> (<font color="Olive" title="b5">fi</font>,<font color="Olive" title="b4">r</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="euclid_9.html#K4" title="EUCLID_9:func.4">OpenHypercube</a> (<font color="Olive" title="b6">fj</font>,<font color="Olive" title="b4">r</font>)</span>)</span></span><a href="borsuk_1.html#K3" title="BORSUK_1:func.3">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="euclid_9.html#K4" title="EUCLID_9:func.4">OpenHypercube</a> (<font color="Olive" title="b7">fij</font>,<font color="Olive" title="b4">r</font>)</div></div>
